# [SI-LIST] : Re: SI-LIST - Self and mutual inductance

Juliusz Poltz ([email protected])
Mon, 4 May 1998 15:40:06 +0000

Monday, May 04, 1998

Hello Lidu,

Since I did not see any comments related to your inductance problem I
decided to send this note.

First of all, I assume that in your example the wavelength is much
larger than the cross-sectional dimensions of the analyzed objects.
Then, I would like to state that we should follow the rule that the
concept of inductance requires closed loop currents.

In 2d it means that one should not analyze a single busbar (one can
assume without analysis that the inductance value is in this case
infinity). One will need a reference conductor for the return current
to calculate reasonable values. However, some software tools may
introduce the return path in some arbitrary location (if it does not
exist in the design sheet) and fool the user that a busbar inductance
is calculated.

One may also separate the magnetic field energy outside conductor and
inside conductor and claim that the total inductance is equal to the
sum of these two terms (inner and outer inductance). Since outer
inductance is infinity in the case of a single busbar, one can
calculate inner inductance and claim that this is the proper value
representing the inductance of a busbar - but this is not correct.
Since skin effect pushes current towards the conductor surface, the
magnetic field is also pushed out of the conductor and therefore inner
inductance is 0 at high frequencies. If you sweep frequency and your
inductance plot approaches 0 for higher frequencies (as in the case of
your diagram) you may be sure that your formula or tool is calculating
the so called inner inductance only.

In 3d the situation can be complicated by the fact that we can find a
(double) integral formula for calculating inductance. Since
integration is nothing else than superposition, this formula can be
used for calculating so called partial inductance of a piece of wire
of busbar. Still the total inductance must include all terms (all
pieces of the circuit) and cannot be calculated until the entire
circuit is known.